009A Sample Midterm 2, Problem 1

Evaluate the following limits.

a) Find $\lim _{x\rightarrow 2}{\frac {{\sqrt {x^{2}+12}}-4}{x-2}}$

b) Find $\lim _{x\rightarrow 0}{\frac {\sin(3x)}{\sin(7x)}}$

c) Evaluate Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim _{x\rightarrow (\frac{\pi}{2})^-} \tan(x) }

Foundations:

Solution:

(a)

Step 1:

Step 2:

(b)

Step 1:

Step 2:

(c)

Step 1:

Step 2:

Final Answer:
(a)
(b)
(c)

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